I think some of this might be to do with the male-female friendship dynamic you have going on, even if it's only a really small part of why you can't seem to let go of him. I'm going to separate him and her in this, because the friendship with her is completely in the past, whereas you're clinging to the one you feel you still have with him.
I agree completely with PP that the relationship with him is toxic. How or why it became that way is almost irrelevant at this point, not to be dismissive but because it's not healthy at this stage and therefore you need to walk away. Agonising over the past and the loyalties isn't helping you: it's sunken cost fallacy. He's not a positive relationship in your life, but you keep referring to 'childhood friendship' and 'like a brother' so you keep going back for more, despite knowing you need weeks to recover from seeing him every time. It shouldn't be that hard. Remove the wife from the scenario entirely, and would you spend time once every two months with someone who made you feel awful and required this much headspace? Something is making you do this, and I think it's martyrdom to the cause of a one-sided friendship that he simply doesn't sink as much headspace into as you do.
The baby wouldn't change things for me. He's just a reason for you to get re-involved, which is why I wouldn't send anything if I were in this scenario. Not to be cruel, but because keeping him at arms length and her completely out of my life would be preserving my own mental health. For me, not sending a gift would be taking back control, and would further acknowledge to my own self that the friendship dynamic the three of us shared is firmly in the past and staying there.
As for the wife, she made her position abundantly clear with her wrecking ball text, and you fell over yourself to take as much blame as possible. Friendships should not be about martyrdom. You say she didn't accept her portion of blame, it sounds like I. Some respects she didn't feel she needed to because you were taking most of it anyway. She has walked away, you're still hurting two full years later. No wonder the husband has you dangling on a string, you're doing exactly the same thing with him only much, much slower - martyring yourself to the friendship hoping he won't leave it and/or badmouth you to everyone. You're emotionally blackmailing yourself. Walking away from him would be hugely freeing for you, you'd finally have control of the situation. Who cares if he tells other people you're a meany? Be truthful, and own it.
Him to mutuals: "Perri won't see me anymore, she's got a problem with me, I have no idea why"
You to mutuals: Tinkly laugh, "oh that? I got fed up of his little digs, and you know Wife and I sadly aren't friends now. People grow up and drift apart... now, what are we having to drink?"
Finally, I do think there's something in this that you're clinging to because you think this male/female friendship dynamic you have is special, possibly because it circumvents the norm. Lots of PP have suggested you're in love with him, or he's got secret feelings for you, but I believe you when you say that's not the case. I think you've both been saying it for donkey's years, assuring outsiders that no, you haven't and never have had feelings for each other, you're like siblings after all, and that's become a big part of your friendship, almost like your 'brand'. So, I think part of you is clinging to him more than you would if this were a woman, because you've always had to defend your friendship on some level and it ending might make people think they've been proved right - that men and women cannot be platonic friends. Please don't hang on in any way just for that, you're not failing if you walk away from him and I genuinely think that's exactly what you need to do. Let it end. Not with a bang, but with a whimper. Just let the text banter die out, become unavailable, and free yourself from all this drama.